Thanks Sartaj. I went through the Expr class and it cleared all my doubts. I actually forgot that Function class is inheriting Expr class.
Regards Sampad Kumar Saha Mathematics and Computing I.I.T. Kharagpur On Wed, Mar 23, 2016 at 4:58 PM, Sartaj Singh <[email protected]> wrote: > Hi, > > This comes from Expr class. > > On 23 March 2016 at 16:55, SAMPAD SAHA <[email protected]> wrote: > >> I am having a big confusion over this. >> >> There is no *integrate()* method defined in *DiracDelta* and* Heaviside. >> *But still how can this happen. >> >> In [ ] : DiracDelta(x).integrate() >> Out [ ] : Heaviside(x) >> >> In [ ] : Heaviside(x).integrate() >> Out [ ] : x*Heaviside(x) >> >> I feel like this should raise error as *AttributeError: 'DiracDelta' >> object has no attribute 'integrate'.* >> >> Please explain how this is happenning. >> >> >> >> Regards >> Sampad Kumar Saha >> Mathematics and Computing >> I.I.T. Kharagpur >> >> On Wed, Mar 23, 2016 at 4:48 AM, SAMPAD SAHA <[email protected]> >> wrote: >> >>> >>> Here is my proposal. >>> >>> https://github.com/sympy/sympy/wiki/GSoC-2016-Application-Sampad-Kumar-Saha:-Singularity-Functions >>> >>> >>> >>> Regards >>> Sampad Kumar Saha >>> Mathematics and Computing >>> I.I.T. Kharagpur >>> >>> On Wed, Mar 23, 2016 at 4:08 AM, SAMPAD SAHA <[email protected]> >>> wrote: >>> >>>> Thanks Jason, I have made some changes. Can you please review those? I >>>> have also added some comments along with yours. >>>> >>>> I didn't get you in this comment. Can you please elaborate it? >>>> "*Comment from Jason: You will need to make sure everything is >>>> backwards compatible. See the wiki for our policy.*" >>>> >>>> >>>> >>>> >>>> Regards >>>> Sampad Kumar Saha >>>> Mathematics and Computing >>>> I.I.T. Kharagpur >>>> >>>> On Tue, Mar 22, 2016 at 8:53 PM, Jason Moore <[email protected]> >>>> wrote: >>>> >>>>> The example you show doesn't seem to reflect what we may actually see >>>>> when using this for beams. I'd suggest picking a simple beam problem and >>>>> showing what all of your code will look like. You did that pretty well for >>>>> the later examples, but this one with the random polynomials wasn't that >>>>> clear. >>>>> >>>>> >>>>> Jason >>>>> moorepants.info >>>>> +01 530-601-9791 >>>>> >>>>> On Tue, Mar 22, 2016 at 7:43 AM, SAMPAD SAHA <[email protected]> >>>>> wrote: >>>>> >>>>>> Thank You Jason. I will put it. >>>>>> >>>>>> I have a doubt about this comment in my proposal : >>>>>> >>>>>> *"Comment from Jason: It would be more informative to show what a >>>>>> beam equation would look like in Piecewise form. This is a little >>>>>> abstract." * >>>>>> >>>>>> Can you explain it a little more? >>>>>> >>>>>> I have also added some comment next to yours, I am still working on >>>>>> some of your comments. >>>>>> >>>>>> Regards >>>>>> Sampad Kumar Saha >>>>>> Mathematics and Computing >>>>>> I.I.T. Kharagpur >>>>>> >>>>>> On Tue, Mar 22, 2016 at 8:08 PM, Jason Moore <[email protected]> >>>>>> wrote: >>>>>> >>>>>>> Sounds good, just put it in your proposal. >>>>>>> >>>>>>> >>>>>>> Jason >>>>>>> moorepants.info >>>>>>> +01 530-601-9791 >>>>>>> >>>>>>> On Tue, Mar 22, 2016 at 7:32 AM, SAMPAD SAHA <[email protected]> >>>>>>> wrote: >>>>>>> >>>>>>>> I will start coding along with community bonding. I will spend 3-4 >>>>>>>> hours extra in the last week of the community bonding period in order >>>>>>>> to >>>>>>>> achieve the proposed target in my proposal. I will have no problem >>>>>>>> managing >>>>>>>> with those extra hours since I will be having Summer break at that >>>>>>>> time and >>>>>>>> along with that I have no other commitments. And I will also have fun >>>>>>>> working those extra hours. >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> Regards >>>>>>>> Sampad Kumar Saha >>>>>>>> Mathematics and Computing >>>>>>>> I.I.T. Kharagpur >>>>>>>> >>>>>>>> On Tue, Mar 22, 2016 at 4:13 AM, Jason Moore <[email protected]> >>>>>>>> wrote: >>>>>>>> >>>>>>>>> No need to cancel your vacation. Just give a plan for how you will >>>>>>>>> make up the days. >>>>>>>>> >>>>>>>>> >>>>>>>>> Jason >>>>>>>>> moorepants.info >>>>>>>>> +01 530-601-9791 >>>>>>>>> >>>>>>>>> On Mon, Mar 21, 2016 at 2:52 PM, SAMPAD SAHA < >>>>>>>>> [email protected]> wrote: >>>>>>>>> >>>>>>>>>> Thank You Jason for the suggestions in my proposal. I will work >>>>>>>>>> on those and let you know as soon as possible. >>>>>>>>>> >>>>>>>>>> I have mentioned in my proposal about the days of the vacation >>>>>>>>>> and how can I compensate the work. If this vacation raises any >>>>>>>>>> problem, I >>>>>>>>>> can cancel it . That will not be a problem for me. I don't want to >>>>>>>>>> let >>>>>>>>>> anything ruin the progess of the project as this Summer of Code will >>>>>>>>>> become >>>>>>>>>> an integral part of all my learning throughout the summer. >>>>>>>>>> >>>>>>>>>> ---------------- >>>>>>>>>> Regards >>>>>>>>>> Sampad >>>>>>>>>> >>>>>>>>>> >>>>>>>>>> Regards >>>>>>>>>> Sampad Kumar Saha >>>>>>>>>> Mathematics and Computing >>>>>>>>>> I.I.T. Kharagpur >>>>>>>>>> >>>>>>>>>> On Tue, Mar 22, 2016 at 2:33 AM, Jason Moore < >>>>>>>>>> [email protected]> wrote: >>>>>>>>>> >>>>>>>>>>> I've put some comments in your proposal. >>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> Jason >>>>>>>>>>> moorepants.info >>>>>>>>>>> +01 530-601-9791 >>>>>>>>>>> >>>>>>>>>>> On Sat, Mar 19, 2016 at 10:58 AM, SAMPAD SAHA < >>>>>>>>>>> [email protected]> wrote: >>>>>>>>>>> >>>>>>>>>>>> Jason, >>>>>>>>>>>> >>>>>>>>>>>> Actually I have misunderstood earlier. >>>>>>>>>>>> >>>>>>>>>>>> I have updated my proposal here >>>>>>>>>>>> <https://github.com/sympy/sympy/wiki/GSoC-2016-Application-Sampad-Kumar-Saha-:-Singularity-Functions> >>>>>>>>>>>> . >>>>>>>>>>>> Can you please review it and suggest me to improve it. >>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> Regards >>>>>>>>>>>> Sampad Kumar Saha >>>>>>>>>>>> Mathematics and Computing >>>>>>>>>>>> I.I.T. Kharagpur >>>>>>>>>>>> >>>>>>>>>>>> On Sat, Mar 19, 2016 at 9:14 PM, Jason Moore < >>>>>>>>>>>> [email protected]> wrote: >>>>>>>>>>>> >>>>>>>>>>>>> I don't think we should do "a hack". If we follow the patterns >>>>>>>>>>>>> in the integration code, we should leave the constants of >>>>>>>>>>>>> integration off. >>>>>>>>>>>>> But in the Beam classes you can have them manage the constants of >>>>>>>>>>>>> integration. What you show above looks fine. >>>>>>>>>>>>> >>>>>>>>>>>>> I didn't mean to use dsolve in any way. I just meant to have a >>>>>>>>>>>>> look at that code because they include constants of integration >>>>>>>>>>>>> when you >>>>>>>>>>>>> solve the ode. You can also set the boundary conditions in the >>>>>>>>>>>>> constructor. >>>>>>>>>>>>> It can give you ideas of how to design your api. >>>>>>>>>>>>> >>>>>>>>>>>>> >>>>>>>>>>>>> Jason >>>>>>>>>>>>> moorepants.info >>>>>>>>>>>>> +01 530-601-9791 >>>>>>>>>>>>> >>>>>>>>>>>>> On Sat, Mar 19, 2016 at 8:27 AM, SAMPAD SAHA < >>>>>>>>>>>>> [email protected]> wrote: >>>>>>>>>>>>> >>>>>>>>>>>>>> Jason, >>>>>>>>>>>>>> >>>>>>>>>>>>>> I went through the ode package. I felt that it would be >>>>>>>>>>>>>> difficult to use boundary condition to solve for the constants of >>>>>>>>>>>>>> integration using the exisiting *dsolve() *method. It seems >>>>>>>>>>>>>> that it is still under development. >>>>>>>>>>>>>> >>>>>>>>>>>>>> So I thought of implementing that functionality explicitly >>>>>>>>>>>>>> for solving beam problems. >>>>>>>>>>>>>> >>>>>>>>>>>>>> I would be taking Boundary conditions as input as: >>>>>>>>>>>>>> >>>>>>>>>>>>>> *bcs = Beam.BoundaryCondition( {f(0) : 5, f.diff(0) : 4 } )* >>>>>>>>>>>>>> and so on. >>>>>>>>>>>>>> >>>>>>>>>>>>>> If nothing is provided then *f(0) != 0 , f.diff(0) = 0 *or >>>>>>>>>>>>>> something like this would be assumed. >>>>>>>>>>>>>> >>>>>>>>>>>>>> Depending on this boundary condition I would add the required >>>>>>>>>>>>>> constants by myself while finding the slope and deflection >>>>>>>>>>>>>> function and >>>>>>>>>>>>>> output the value by solving for those constants. >>>>>>>>>>>>>> >>>>>>>>>>>>>> By this way, the hack would be easier. What do you suggests? >>>>>>>>>>>>>> >>>>>>>>>>>>>> >>>>>>>>>>>>>> >>>>>>>>>>>>>> >>>>>>>>>>>>>> >>>>>>>>>>>>>> >>>>>>>>>>>>>> Regards >>>>>>>>>>>>>> Sampad Kumar Saha >>>>>>>>>>>>>> Mathematics and Computing >>>>>>>>>>>>>> I.I.T. Kharagpur >>>>>>>>>>>>>> >>>>>>>>>>>>>> On Sat, Mar 19, 2016 at 7:17 AM, SAMPAD SAHA < >>>>>>>>>>>>>> [email protected]> wrote: >>>>>>>>>>>>>> >>>>>>>>>>>>>>> Yah, you are right . We should not have the name simplify() >>>>>>>>>>>>>>> as a method since it have already created some issues in >>>>>>>>>>>>>>> #7716 <https://github.com/sympy/sympy/issues/7716> and #8798 >>>>>>>>>>>>>>> <https://github.com/sympy/sympy/issues/8798>. So i will >>>>>>>>>>>>>>> keep it as *to_piecewise()* . it would be fine then. >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> As you suggested I will be look at ode package for this >>>>>>>>>>>>>>> constant of integration thing. >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> Thank You... >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> Regards >>>>>>>>>>>>>>> Sampad Kumar Saha >>>>>>>>>>>>>>> Mathematics and Computing >>>>>>>>>>>>>>> I.I.T. Kharagpur >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> On Sat, Mar 19, 2016 at 7:07 AM, Jason Moore < >>>>>>>>>>>>>>> [email protected]> wrote: >>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> Simplification means something very specific in SymPy, see >>>>>>>>>>>>>>>> the simplify() function. I think you need to choose a >>>>>>>>>>>>>>>> different method name >>>>>>>>>>>>>>>> for converting to piecewise continuous. Maybe: .to_piecewise()? >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> You will need to implement some method for dealing with the >>>>>>>>>>>>>>>> constants of integration and boundary conditions. Maybe you >>>>>>>>>>>>>>>> should have a >>>>>>>>>>>>>>>> look at the ordinary differential equations package in SymPy >>>>>>>>>>>>>>>> to get some >>>>>>>>>>>>>>>> ideas about that. >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> Jason >>>>>>>>>>>>>>>> moorepants.info >>>>>>>>>>>>>>>> +01 530-601-9791 >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> On Fri, Mar 18, 2016 at 4:04 PM, SAMPAD SAHA < >>>>>>>>>>>>>>>> [email protected]> wrote: >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> Thank You Jason for the appreciation. >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> Yah, that *Simplify * method would convert into >>>>>>>>>>>>>>>>> continous piecewise. Like this :- >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> In [ ] : F = singularityFunc(x, 0, 1) + >>>>>>>>>>>>>>>>> singularityFunc(x, 3, 2) >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> In [ ] : F >>>>>>>>>>>>>>>>> Out [ ] : >>>>>>>>>>>>>>>>> 2 >>>>>>>>>>>>>>>>> <x> + <x - 3> >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> In [ ] : F.simplify() >>>>>>>>>>>>>>>>> Out [ ] : >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> 0 for x < 0 >>>>>>>>>>>>>>>>> x for 0 <= x < 3 >>>>>>>>>>>>>>>>> x + (x-3)^2 for x >= 3 >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> As you have suggested earlier, I have solved some examples >>>>>>>>>>>>>>>>> by hand and then tried to implement a desired api. From that >>>>>>>>>>>>>>>>> I came to this >>>>>>>>>>>>>>>>> conclusion that if we implement Addition, Substraction, >>>>>>>>>>>>>>>>> Integration, Differentiation, Simplify on Singularity >>>>>>>>>>>>>>>>> Functions then we can >>>>>>>>>>>>>>>>> successfully solve out the beam problems. >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> But i got doubt while implementing the boundary constants. >>>>>>>>>>>>>>>>> I mean to say that sympy dont gives constant of integration >>>>>>>>>>>>>>>>> while doing >>>>>>>>>>>>>>>>> indefinite integration. We can take boundary conditions as >>>>>>>>>>>>>>>>> input from users >>>>>>>>>>>>>>>>> that is not a problem, but we cant use it since there will be >>>>>>>>>>>>>>>>> no constant >>>>>>>>>>>>>>>>> of integration. >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> Regards >>>>>>>>>>>>>>>>> Sampad Kumar Saha >>>>>>>>>>>>>>>>> Mathematics and Computing >>>>>>>>>>>>>>>>> I.I.T. Kharagpur >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> On Sat, Mar 19, 2016 at 4:07 AM, Jason Moore < >>>>>>>>>>>>>>>>> [email protected]> wrote: >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>> Sounds like a good start. How about a method to convert >>>>>>>>>>>>>>>>>> to continuous piecewise? >>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>> Like I said earlier, you should pick some examples that >>>>>>>>>>>>>>>>>> you want the software to be able to solve and then implement >>>>>>>>>>>>>>>>>> methods and >>>>>>>>>>>>>>>>>> functionality based on those examples. It's hard to think of >>>>>>>>>>>>>>>>>> all the needed >>>>>>>>>>>>>>>>>> functionality and API without motivating examples first. >>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>> Jason >>>>>>>>>>>>>>>>>> moorepants.info >>>>>>>>>>>>>>>>>> +01 530-601-9791 >>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>> On Fri, Mar 18, 2016 at 10:27 AM, SAMPAD SAHA < >>>>>>>>>>>>>>>>>> [email protected]> wrote: >>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>> Jason, >>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>> I have thought of implementing Addition, Substraction, >>>>>>>>>>>>>>>>>>> Integration, Differentiation, Simplify on Singularity >>>>>>>>>>>>>>>>>>> Functions. >>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>> What are the other functionalities we should implement? >>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>> Regards >>>>>>>>>>>>>>>>>>> Sampad Kumar Saha >>>>>>>>>>>>>>>>>>> Mathematics and Computing >>>>>>>>>>>>>>>>>>> I.I.T. Kharagpur >>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>> On Fri, Mar 18, 2016 at 8:16 PM, SAMPAD SAHA < >>>>>>>>>>>>>>>>>>> [email protected]> wrote: >>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>> Yah you are correct. Differentiation of heaviside and >>>>>>>>>>>>>>>>>>>> diracdelta also exists. >>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>> It was my mistake. Thanks for rectifying me. >>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>> Regards >>>>>>>>>>>>>>>>>>>> Sampad Kumar Saha >>>>>>>>>>>>>>>>>>>> Mathematics and Computing >>>>>>>>>>>>>>>>>>>> I.I.T. Kharagpur >>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>> On Fri, Mar 18, 2016 at 8:02 PM, Tim Lahey < >>>>>>>>>>>>>>>>>>>> [email protected]> wrote: >>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>> For differentiation you’re missing a case, >>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>> if n = 0 or n = -1 >>>>>>>>>>>>>>>>>>>>> return Singularity(x, a, n-1) >>>>>>>>>>>>>>>>>>>>> else if n < -1 >>>>>>>>>>>>>>>>>>>>> return error >>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>> In other words, you can still differentiate for the n >>>>>>>>>>>>>>>>>>>>> = 0 and n = -1 cases. >>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>> Cheers, >>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>> Tim. >>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>> > On Mar 18, 2016, at 10:22 AM, SAMPAD SAHA < >>>>>>>>>>>>>>>>>>>>> [email protected]> wrote: >>>>>>>>>>>>>>>>>>>>> > >>>>>>>>>>>>>>>>>>>>> > And what about the pseudocode of integration and >>>>>>>>>>>>>>>>>>>>> differentiation i have posted earlier , is it alright? >>>>>>>>>>>>>>>>>>>>> > >>>>>>>>>>>>>>>>>>>>> > >>>>>>>>>>>>>>>>>>>>> > >>>>>>>>>>>>>>>>>>>>> > >>>>>>>>>>>>>>>>>>>>> > >>>>>>>>>>>>>>>>>>>>> > Regards >>>>>>>>>>>>>>>>>>>>> > Sampad Kumar Saha >>>>>>>>>>>>>>>>>>>>> > Mathematics and Computing >>>>>>>>>>>>>>>>>>>>> > I.I.T. Kharagpur >>>>>>>>>>>>>>>>>>>>> > >>>>>>>>>>>>>>>>>>>>> > On Fri, Mar 18, 2016 at 7:51 PM, SAMPAD SAHA < >>>>>>>>>>>>>>>>>>>>> [email protected]> wrote: >>>>>>>>>>>>>>>>>>>>> > Thanks Tim, >>>>>>>>>>>>>>>>>>>>> > >>>>>>>>>>>>>>>>>>>>> > It is really a nice and effective solution. >>>>>>>>>>>>>>>>>>>>> > >>>>>>>>>>>>>>>>>>>>> > >>>>>>>>>>>>>>>>>>>>> > >>>>>>>>>>>>>>>>>>>>> > >>>>>>>>>>>>>>>>>>>>> > >>>>>>>>>>>>>>>>>>>>> > Regards >>>>>>>>>>>>>>>>>>>>> > Sampad Kumar Saha >>>>>>>>>>>>>>>>>>>>> > Mathematics and Computing >>>>>>>>>>>>>>>>>>>>> > I.I.T. Kharagpur >>>>>>>>>>>>>>>>>>>>> > >>>>>>>>>>>>>>>>>>>>> > On Fri, Mar 18, 2016 at 7:46 PM, Tim Lahey < >>>>>>>>>>>>>>>>>>>>> [email protected]> wrote: >>>>>>>>>>>>>>>>>>>>> > Add the constants when you integrate in your beam >>>>>>>>>>>>>>>>>>>>> class. >>>>>>>>>>>>>>>>>>>>> > >>>>>>>>>>>>>>>>>>>>> > >>>>>>>>>>>>>>>>>>>>> > On 2016-03-18, at 10:12 AM, SAMPAD SAHA < >>>>>>>>>>>>>>>>>>>>> [email protected]> wrote: >>>>>>>>>>>>>>>>>>>>> > >>>>>>>>>>>>>>>>>>>>> >> Thanks TIm, >>>>>>>>>>>>>>>>>>>>> >> >>>>>>>>>>>>>>>>>>>>> >> Integration and Differentiation are really very >>>>>>>>>>>>>>>>>>>>> straight forward that is why i am thinking to add diff >>>>>>>>>>>>>>>>>>>>> and integrate method >>>>>>>>>>>>>>>>>>>>> to the Singularity function class itself. >>>>>>>>>>>>>>>>>>>>> >> >>>>>>>>>>>>>>>>>>>>> >> For integrate the pseuesocode will be :- >>>>>>>>>>>>>>>>>>>>> >> >>>>>>>>>>>>>>>>>>>>> >> if(n<0) >>>>>>>>>>>>>>>>>>>>> >> return SingularityFunction(x , a, n+1) >>>>>>>>>>>>>>>>>>>>> >> else >>>>>>>>>>>>>>>>>>>>> >> return (1/n+1 * SingularityFunction(x , a, n+1)) >>>>>>>>>>>>>>>>>>>>> >> >>>>>>>>>>>>>>>>>>>>> >> Similarly for differentiation: >>>>>>>>>>>>>>>>>>>>> >> >>>>>>>>>>>>>>>>>>>>> >> if (n>0) >>>>>>>>>>>>>>>>>>>>> >> return n * SingularityFunction(x , a, n - 1) >>>>>>>>>>>>>>>>>>>>> >> else >>>>>>>>>>>>>>>>>>>>> >> Error message >>>>>>>>>>>>>>>>>>>>> >> >>>>>>>>>>>>>>>>>>>>> >> >>>>>>>>>>>>>>>>>>>>> >> My doubt regarding Boundary condition was actually >>>>>>>>>>>>>>>>>>>>> was that since sympy don't provide constant of >>>>>>>>>>>>>>>>>>>>> integration while performing >>>>>>>>>>>>>>>>>>>>> indefinite integration on any expression, how to use the >>>>>>>>>>>>>>>>>>>>> boundary >>>>>>>>>>>>>>>>>>>>> conditions to find the exact values of constant of >>>>>>>>>>>>>>>>>>>>> integration? >>>>>>>>>>>>>>>>>>>>> >> >>>>>>>>>>>>>>>>>>>>> >> >>>>>>>>>>>>>>>>>>>>> >> >>>>>>>>>>>>>>>>>>>>> >> >>>>>>>>>>>>>>>>>>>>> >> >>>>>>>>>>>>>>>>>>>>> >> Regards >>>>>>>>>>>>>>>>>>>>> >> Sampad Kumar Saha >>>>>>>>>>>>>>>>>>>>> >> Mathematics and Computing >>>>>>>>>>>>>>>>>>>>> >> I.I.T. Kharagpur >>>>>>>>>>>>>>>>>>>>> >> >>>>>>>>>>>>>>>>>>>>> >> On Fri, Mar 18, 2016 at 6:09 PM, Tim Lahey < >>>>>>>>>>>>>>>>>>>>> [email protected]> wrote: >>>>>>>>>>>>>>>>>>>>> >> Hi, >>>>>>>>>>>>>>>>>>>>> >> >>>>>>>>>>>>>>>>>>>>> >> Do you know the integration and differentiation >>>>>>>>>>>>>>>>>>>>> rules for singularity functions? They’re pretty >>>>>>>>>>>>>>>>>>>>> straightforward. >>>>>>>>>>>>>>>>>>>>> >> >>>>>>>>>>>>>>>>>>>>> >> As for boundary conditions, the beam will have >>>>>>>>>>>>>>>>>>>>> supports (or a free end) at each end of the beam and as >>>>>>>>>>>>>>>>>>>>> part of the beam >>>>>>>>>>>>>>>>>>>>> creation each end type is specified. Each type >>>>>>>>>>>>>>>>>>>>> corresponds to a specific >>>>>>>>>>>>>>>>>>>>> set of conditions on that end (either at x=0 or x=L). You >>>>>>>>>>>>>>>>>>>>> substitute those >>>>>>>>>>>>>>>>>>>>> conditions in the appropriate equation and solve for the >>>>>>>>>>>>>>>>>>>>> integration >>>>>>>>>>>>>>>>>>>>> constant as necessary. All of the conditions should be in >>>>>>>>>>>>>>>>>>>>> any decent >>>>>>>>>>>>>>>>>>>>> mechanics of deformable solids text book. >>>>>>>>>>>>>>>>>>>>> >> >>>>>>>>>>>>>>>>>>>>> >> You’ll want to do sums of forces and moments as >>>>>>>>>>>>>>>>>>>>> well to solve for reaction forces as well. >>>>>>>>>>>>>>>>>>>>> >> >>>>>>>>>>>>>>>>>>>>> >> The only trick is making sure you don’t double >>>>>>>>>>>>>>>>>>>>> count things. If you have a step function due to a >>>>>>>>>>>>>>>>>>>>> reaction force at the >>>>>>>>>>>>>>>>>>>>> start of the beam and assume it’s zero at x=0 >>>>>>>>>>>>>>>>>>>>> (effectively the limit at >>>>>>>>>>>>>>>>>>>>> x=0^-) you can get a non-zero integration constant that >>>>>>>>>>>>>>>>>>>>> can be double >>>>>>>>>>>>>>>>>>>>> counting that reaction since at x=0^+ that reaction force >>>>>>>>>>>>>>>>>>>>> is non-zero. Note >>>>>>>>>>>>>>>>>>>>> that you can get a non-zero integration constant (even >>>>>>>>>>>>>>>>>>>>> when including >>>>>>>>>>>>>>>>>>>>> reaction forces in the loading function) for shear and >>>>>>>>>>>>>>>>>>>>> moment equations if >>>>>>>>>>>>>>>>>>>>> you have non-polynomial loads (e.g., sine and cosine). >>>>>>>>>>>>>>>>>>>>> You’ll also have to >>>>>>>>>>>>>>>>>>>>> think about the other end as well. I leave it up to you >>>>>>>>>>>>>>>>>>>>> to reason that out. >>>>>>>>>>>>>>>>>>>>> Make sure you completely document how you’ve implemented >>>>>>>>>>>>>>>>>>>>> it for the user >>>>>>>>>>>>>>>>>>>>> (and why). >>>>>>>>>>>>>>>>>>>>> >> >>>>>>>>>>>>>>>>>>>>> >> Beam coordinate systems must start at the left end >>>>>>>>>>>>>>>>>>>>> and increase to the right. The definition of the >>>>>>>>>>>>>>>>>>>>> singularity functions >>>>>>>>>>>>>>>>>>>>> require this. >>>>>>>>>>>>>>>>>>>>> >> >>>>>>>>>>>>>>>>>>>>> >> I hope this helps. >>>>>>>>>>>>>>>>>>>>> >> >>>>>>>>>>>>>>>>>>>>> >> Cheers, >>>>>>>>>>>>>>>>>>>>> >> >>>>>>>>>>>>>>>>>>>>> >> Tim. >>>>>>>>>>>>>>>>>>>>> >> >>>>>>>>>>>>>>>>>>>>> >> > On Mar 18, 2016, at 8:17 AM, SAMPAD SAHA < >>>>>>>>>>>>>>>>>>>>> [email protected]> wrote: >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > I am also confused about implementing the >>>>>>>>>>>>>>>>>>>>> boundary conditions for getting the deflection curve. >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > Any suggestions on how to implement it. >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > Regards >>>>>>>>>>>>>>>>>>>>> >> > Sampad Kumar Saha >>>>>>>>>>>>>>>>>>>>> >> > Mathematics and Computing >>>>>>>>>>>>>>>>>>>>> >> > I.I.T. Kharagpur >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > On Fri, Mar 18, 2016 at 5:36 PM, SAMPAD SAHA < >>>>>>>>>>>>>>>>>>>>> [email protected]> wrote: >>>>>>>>>>>>>>>>>>>>> >> > Yah, you are right multiplication of singularity >>>>>>>>>>>>>>>>>>>>> functions are not needed for solving beam problems. >>>>>>>>>>>>>>>>>>>>> Mathematically, it is >>>>>>>>>>>>>>>>>>>>> also not used that much. So lets leave this >>>>>>>>>>>>>>>>>>>>> multiplication and powers part. >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > I was thinking about the integrate and diff >>>>>>>>>>>>>>>>>>>>> methods. I feel that we should define instance methods >>>>>>>>>>>>>>>>>>>>> diff and integrate >>>>>>>>>>>>>>>>>>>>> in the singularity function module which would internally >>>>>>>>>>>>>>>>>>>>> use the existing >>>>>>>>>>>>>>>>>>>>> diff and integrate function for Differentiation and >>>>>>>>>>>>>>>>>>>>> Integration >>>>>>>>>>>>>>>>>>>>> respectively. >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > I need your suggestions. >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > Regards >>>>>>>>>>>>>>>>>>>>> >> > Sampad Kumar Saha >>>>>>>>>>>>>>>>>>>>> >> > Mathematics and Computing >>>>>>>>>>>>>>>>>>>>> >> > I.I.T. Kharagpur >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > On Fri, Mar 18, 2016 at 3:14 AM, Jason Moore < >>>>>>>>>>>>>>>>>>>>> [email protected]> wrote: >>>>>>>>>>>>>>>>>>>>> >> > I think you need to override the operators. I'm >>>>>>>>>>>>>>>>>>>>> not sure if multiplying singularity functions is needed >>>>>>>>>>>>>>>>>>>>> (at least for beam >>>>>>>>>>>>>>>>>>>>> problems), even if it is mathematically correct, you >>>>>>>>>>>>>>>>>>>>> don't have to >>>>>>>>>>>>>>>>>>>>> implement it. If it is easy to implement then, sure, do >>>>>>>>>>>>>>>>>>>>> so. >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > Jason >>>>>>>>>>>>>>>>>>>>> >> > moorepants.info >>>>>>>>>>>>>>>>>>>>> >> > +01 530-601-9791 >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > On Thu, Mar 17, 2016 at 1:34 PM, SAMPAD SAHA < >>>>>>>>>>>>>>>>>>>>> [email protected]> wrote: >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > Jason, >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > For implementing Additon , Multiplication Do we >>>>>>>>>>>>>>>>>>>>> need to over ride __mul__ , __add__ these methods inside >>>>>>>>>>>>>>>>>>>>> the class >>>>>>>>>>>>>>>>>>>>> SingularityFunction or we can just use simplify for >>>>>>>>>>>>>>>>>>>>> getting the results. >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > I am really confused. >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > Regards >>>>>>>>>>>>>>>>>>>>> >> > Sampad Kumar Saha >>>>>>>>>>>>>>>>>>>>> >> > Mathematics and Computing >>>>>>>>>>>>>>>>>>>>> >> > I.I.T. Kharagpur >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > On Fri, Mar 18, 2016 at 1:59 AM, SAMPAD SAHA < >>>>>>>>>>>>>>>>>>>>> [email protected]> wrote: >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > I was thinking about multiplication of two >>>>>>>>>>>>>>>>>>>>> singularity functions. It is possible and it is >>>>>>>>>>>>>>>>>>>>> mathematically significant. >>>>>>>>>>>>>>>>>>>>> We can implement this too in Sympy. Similarly with powers. >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > I need your suggestions. >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > Regards >>>>>>>>>>>>>>>>>>>>> >> > Sampad Kumar Saha >>>>>>>>>>>>>>>>>>>>> >> > Mathematics and Computing >>>>>>>>>>>>>>>>>>>>> >> > I.I.T. Kharagpur >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > On Wed, Mar 16, 2016 at 9:41 PM, SAMPAD SAHA < >>>>>>>>>>>>>>>>>>>>> [email protected]> wrote: >>>>>>>>>>>>>>>>>>>>> >> > Yah , You are right . A software having good >>>>>>>>>>>>>>>>>>>>> documentations about all the functionality is preffered >>>>>>>>>>>>>>>>>>>>> more over the >>>>>>>>>>>>>>>>>>>>> others by the users. I will be spending a good amount of >>>>>>>>>>>>>>>>>>>>> time in preparing >>>>>>>>>>>>>>>>>>>>> the documentation citing plenty of examples and tutorials. >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > Here is link to my proposal. I have almost added >>>>>>>>>>>>>>>>>>>>> all the things which we have disscussed. I still need to >>>>>>>>>>>>>>>>>>>>> add the example >>>>>>>>>>>>>>>>>>>>> and many more "TODO"s are left. I am working on those. >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > Suggestions are welcomed. >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > Regards >>>>>>>>>>>>>>>>>>>>> >> > Sampad Kumar Saha >>>>>>>>>>>>>>>>>>>>> >> > Mathematics and Computing >>>>>>>>>>>>>>>>>>>>> >> > I.I.T. Kharagpur >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > On Wed, Mar 16, 2016 at 6:18 AM, Jason Moore < >>>>>>>>>>>>>>>>>>>>> [email protected]> wrote: >>>>>>>>>>>>>>>>>>>>> >> > Looks good. I think you should have plenty of >>>>>>>>>>>>>>>>>>>>> examples in the docs. People tend to use software more if >>>>>>>>>>>>>>>>>>>>> the docs are top >>>>>>>>>>>>>>>>>>>>> notch. So plenty of examples and tutorials will really >>>>>>>>>>>>>>>>>>>>> help. >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > Jason >>>>>>>>>>>>>>>>>>>>> >> > moorepants.info >>>>>>>>>>>>>>>>>>>>> >> > +01 530-601-9791 >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > On Tue, Mar 15, 2016 at 5:25 PM, SAMPAD SAHA < >>>>>>>>>>>>>>>>>>>>> [email protected]> wrote: >>>>>>>>>>>>>>>>>>>>> >> > You are right. delta_function.py needs to be >>>>>>>>>>>>>>>>>>>>> improved. I will to be using only DiracDelta and >>>>>>>>>>>>>>>>>>>>> Heaviside for generating >>>>>>>>>>>>>>>>>>>>> almost all the Singularity Functions. >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > I was also thinking to complete this project in >>>>>>>>>>>>>>>>>>>>> four phases: >>>>>>>>>>>>>>>>>>>>> >> > • Improving existiing Functions. >>>>>>>>>>>>>>>>>>>>> >> > • Creating Singularity Functions module >>>>>>>>>>>>>>>>>>>>> >> > • Creating beam Module >>>>>>>>>>>>>>>>>>>>> >> > • Documentation >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > Regards >>>>>>>>>>>>>>>>>>>>> >> > Sampad Kumar Saha >>>>>>>>>>>>>>>>>>>>> >> > Mathematics and Computing >>>>>>>>>>>>>>>>>>>>> >> > I.I.T. Kharagpur >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > On Wed, Mar 16, 2016 at 5:44 AM, Jason Moore < >>>>>>>>>>>>>>>>>>>>> [email protected]> wrote: >>>>>>>>>>>>>>>>>>>>> >> > https://www.python.org/dev/peps/pep-0008/ >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > I think you will need a pure singularity function >>>>>>>>>>>>>>>>>>>>> module and then you will need a beam module that utlizes >>>>>>>>>>>>>>>>>>>>> the singularity >>>>>>>>>>>>>>>>>>>>> function module. You will also likely need to improve the >>>>>>>>>>>>>>>>>>>>> discontinuous >>>>>>>>>>>>>>>>>>>>> functions that are already in sympy. There are at least >>>>>>>>>>>>>>>>>>>>> three layers to >>>>>>>>>>>>>>>>>>>>> this in my eyes. >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > Jason >>>>>>>>>>>>>>>>>>>>> >> > moorepants.info >>>>>>>>>>>>>>>>>>>>> >> > +01 530-601-9791 >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > On Tue, Mar 15, 2016 at 5:07 PM, SAMPAD SAHA < >>>>>>>>>>>>>>>>>>>>> [email protected]> wrote: >>>>>>>>>>>>>>>>>>>>> >> > Jason >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > Pardon please. I couldn't get you by "You will >>>>>>>>>>>>>>>>>>>>> need to follow PEP8 for the method and class names". >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > and yah, i also felt that it would be better if i >>>>>>>>>>>>>>>>>>>>> use the input and output values of the example problem >>>>>>>>>>>>>>>>>>>>> done by hand. >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > So , what do you suggest, Would it be better if >>>>>>>>>>>>>>>>>>>>> we create a different module ,other than the singularity >>>>>>>>>>>>>>>>>>>>> function module, >>>>>>>>>>>>>>>>>>>>> for solving beam problems? That module would import the >>>>>>>>>>>>>>>>>>>>> singularity >>>>>>>>>>>>>>>>>>>>> function module for using them. >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > Regards >>>>>>>>>>>>>>>>>>>>> >> > Sampad Kumar Saha >>>>>>>>>>>>>>>>>>>>> >> > Mathematics and Computing >>>>>>>>>>>>>>>>>>>>> >> > I.I.T. Kharagpur >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > On Wed, Mar 16, 2016 at 5:22 AM, Jason Moore < >>>>>>>>>>>>>>>>>>>>> [email protected]> wrote: >>>>>>>>>>>>>>>>>>>>> >> > I think it is a good start. You will need to >>>>>>>>>>>>>>>>>>>>> follow PEP8 for the method and class names. But I just >>>>>>>>>>>>>>>>>>>>> want to see desired >>>>>>>>>>>>>>>>>>>>> functionality. The more you can think up, the better. I >>>>>>>>>>>>>>>>>>>>> would suggest doing >>>>>>>>>>>>>>>>>>>>> a beam problem by hand and then translating that to a >>>>>>>>>>>>>>>>>>>>> desired API. You can >>>>>>>>>>>>>>>>>>>>> mock up what you think the inputs and outputs should be >>>>>>>>>>>>>>>>>>>>> for that example >>>>>>>>>>>>>>>>>>>>> problem. >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > Jason >>>>>>>>>>>>>>>>>>>>> >> > moorepants.info >>>>>>>>>>>>>>>>>>>>> >> > +01 530-601-9791 >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > On Tue, Mar 15, 2016 at 4:46 PM, SAMPAD SAHA < >>>>>>>>>>>>>>>>>>>>> [email protected]> wrote: >>>>>>>>>>>>>>>>>>>>> >> > Ok Jason, >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > And what about the API I have posted just before >>>>>>>>>>>>>>>>>>>>> the earlier post? >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > Any suggestions >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > Regards >>>>>>>>>>>>>>>>>>>>> >> > Sampad Kumar Saha >>>>>>>>>>>>>>>>>>>>> >> > Mathematics and Computing >>>>>>>>>>>>>>>>>>>>> >> > I.I.T. Kharagpur >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > On Wed, Mar 16, 2016 at 5:10 AM, Jason Moore < >>>>>>>>>>>>>>>>>>>>> [email protected]> wrote: >>>>>>>>>>>>>>>>>>>>> >> > The file locations and method class names are >>>>>>>>>>>>>>>>>>>>> just fine details that can be worked out later. They are >>>>>>>>>>>>>>>>>>>>> generally not >>>>>>>>>>>>>>>>>>>>> important for your proposal. Just focus on describing >>>>>>>>>>>>>>>>>>>>> what the future >>>>>>>>>>>>>>>>>>>>> modules should do. >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > Jason >>>>>>>>>>>>>>>>>>>>> >> > moorepants.info >>>>>>>>>>>>>>>>>>>>> >> > +01 530-601-9791 >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > On Tue, Mar 15, 2016 at 4:36 PM, SAMPAD SAHA < >>>>>>>>>>>>>>>>>>>>> [email protected]> wrote: >>>>>>>>>>>>>>>>>>>>> >> > Hi Jason, >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > As I am thinking to create a another module for >>>>>>>>>>>>>>>>>>>>> solving especially beam problems (suppose beambending.py) >>>>>>>>>>>>>>>>>>>>> , what will be >>>>>>>>>>>>>>>>>>>>> its file location? >>>>>>>>>>>>>>>>>>>>> >> > Similarly for Singularity Functions (suppose >>>>>>>>>>>>>>>>>>>>> singularity_function.py), What will be its location? >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > And what about the names of methods and classes, >>>>>>>>>>>>>>>>>>>>> Can I give any name or we will be discussing it at the >>>>>>>>>>>>>>>>>>>>> time of developing >>>>>>>>>>>>>>>>>>>>> them? >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > --------------------- >>>>>>>>>>>>>>>>>>>>> >> > Regards, >>>>>>>>>>>>>>>>>>>>> >> > Sampad >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > Regards >>>>>>>>>>>>>>>>>>>>> >> > Sampad Kumar Saha >>>>>>>>>>>>>>>>>>>>> >> > Mathematics and Computing >>>>>>>>>>>>>>>>>>>>> >> > I.I.T. Kharagpur >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > On Wed, Mar 16, 2016 at 3:56 AM, SAMPAD SAHA < >>>>>>>>>>>>>>>>>>>>> [email protected]> wrote: >>>>>>>>>>>>>>>>>>>>> >> > Thank You Tim and Jason for your suggestions and >>>>>>>>>>>>>>>>>>>>> clearing my doubts. >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > We can also have an another module for solving >>>>>>>>>>>>>>>>>>>>> beam problems. As Jason Have suggested earlier. >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > Some of its classes would be Beam, >>>>>>>>>>>>>>>>>>>>> DistributedLoad, PointLoad, Moment. >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > We can have the API as:- >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > from sympy import >>>>>>>>>>>>>>>>>>>>> SingularityFunction,Beam,DistributedLoad,PointLoad,Moment >>>>>>>>>>>>>>>>>>>>> >> > b = Beam(length = 1, E = 1.87, I = 12) >>>>>>>>>>>>>>>>>>>>> >> > Load1 = DistrubutedLoad(start=l/2, end=l, value= >>>>>>>>>>>>>>>>>>>>> 50) >>>>>>>>>>>>>>>>>>>>> >> > Load2 = PointLoad(location=l/3, value=60) >>>>>>>>>>>>>>>>>>>>> >> > Load3 = Moment(locaton = 1, value = 40, >>>>>>>>>>>>>>>>>>>>> anticlockwise = True) >>>>>>>>>>>>>>>>>>>>> >> > b.apply(Load1,Load2,Load3) >>>>>>>>>>>>>>>>>>>>> >> > b.loadDistribution # Outputs the loading >>>>>>>>>>>>>>>>>>>>> function in the form of singularity function >>>>>>>>>>>>>>>>>>>>> >> > b.shearForce # Outputs the Shear Force >>>>>>>>>>>>>>>>>>>>> Function >>>>>>>>>>>>>>>>>>>>> >> > b.bendingMoment # Outputs the bending >>>>>>>>>>>>>>>>>>>>> Moment Function >>>>>>>>>>>>>>>>>>>>> >> > b.slope # Outputs the Slope Function >>>>>>>>>>>>>>>>>>>>> >> > b.deflection # Outputs the deflection >>>>>>>>>>>>>>>>>>>>> Function >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > b.plotLoadDistribution # Outputs the plot of >>>>>>>>>>>>>>>>>>>>> load Distribution Curve >>>>>>>>>>>>>>>>>>>>> >> > b.plotBendingMoment # Outputs the plot of >>>>>>>>>>>>>>>>>>>>> Bending Moment Curve >>>>>>>>>>>>>>>>>>>>> >> > b.plotDeflection # Outputs the plot of >>>>>>>>>>>>>>>>>>>>> Deflection Curve >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > Regards >>>>>>>>>>>>>>>>>>>>> >> > Sampad Kumar Saha >>>>>>>>>>>>>>>>>>>>> >> > Mathematics and Computing >>>>>>>>>>>>>>>>>>>>> >> > I.I.T. Kharagpur >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > On Wed, Mar 16, 2016 at 2:45 AM, Tim Lahey < >>>>>>>>>>>>>>>>>>>>> [email protected]> wrote: >>>>>>>>>>>>>>>>>>>>> >> > I agree. One should start directly from the >>>>>>>>>>>>>>>>>>>>> loading function q(x). The general steps are: >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > 1. Start with the loading function q(x) >>>>>>>>>>>>>>>>>>>>> >> > 2. Integrate to get the shear function V(x). >>>>>>>>>>>>>>>>>>>>> >> > 3. Integrate again to get the bending moment >>>>>>>>>>>>>>>>>>>>> function M(x). >>>>>>>>>>>>>>>>>>>>> >> > 4. Integrate to get the slope function E*I*v’(x). >>>>>>>>>>>>>>>>>>>>> >> > 5. Integrate to get the displacement function >>>>>>>>>>>>>>>>>>>>> E*I*v(x). >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > Note that the singularity functions can be >>>>>>>>>>>>>>>>>>>>> multiplied by arbitrary functions of x as well. This >>>>>>>>>>>>>>>>>>>>> allows for varied >>>>>>>>>>>>>>>>>>>>> loads and cases where E and I vary too. To be strictly >>>>>>>>>>>>>>>>>>>>> correct one should >>>>>>>>>>>>>>>>>>>>> include the integration constants as well and then solve >>>>>>>>>>>>>>>>>>>>> for the reaction >>>>>>>>>>>>>>>>>>>>> forces and the constants. >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > You’ll need to carefully consider how you handle >>>>>>>>>>>>>>>>>>>>> evaluating at transition points, especially the beam >>>>>>>>>>>>>>>>>>>>> boundaries. >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > Cheers, >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > Tim. >>>>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>>>> >> > > On Mar 15, 2016, at 4:53 PM, Jason Moore < >>>>>>>>>>>>>>>>>>>>> [email protected]> wrote: >>>>>>>>>>>>>>>>>>>>> >> > > >>>>>>>>>>>>>>>>>>>>> >> > > I think you'd want the user to input the loads >>>>>>>>>>>>>>>>>>>>> on the beam as singularity functions or some higher level >>>>>>>>>>>>>>>>>>>>> abstraction. If >>>>>>>>>>>>>>>>>>>>> you require them to manually compute the bending moment >>>>>>>>>>>>>>>>>>>>> then you are >>>>>>>>>>>>>>>>>>>>> defeating the purpose of having a CAS do it for you. >>>>>>>>>>>>>>>>>>>>> >> > > >>>>>>>>>>>>>>>>>>>>> >> > > >>>>>>>>>>>>>>>>>>>>> >> > > Jason >>>>>>>>>>>>>>>>>>>>> >> > > moorepants.info >>>>>>>>>>>>>>>>>>>>> >> > > +01 530-601-9791 >>>>>>>>>>>>>>>>>>>>> >> > > >>>>>>>>>>>>>>>>>>>>> >> > > On Sun, Mar 13, 2016 at 2:25 PM, SAMPAD SAHA < >>>>>>>>>>>>>>>>>>>>> [email protected]> wrote: >>>>>>>>>>>>>>>>>>>>> >> > > Hi Jason, >>>>>>>>>>>>>>>>>>>>> >> > > >>>>>>>>>>>>>>>>>>>>> >> > > I have a confusion regarding the user inputs >>>>>>>>>>>>>>>>>>>>> for the beam problems. >>>>>>>>>>>>>>>>>>>>> >> > > >>>>>>>>>>>>>>>>>>>>> >> > > I think that we should take only the Bending >>>>>>>>>>>>>>>>>>>>> Moment Function (in the form of singularity functions) >>>>>>>>>>>>>>>>>>>>> and the boundary >>>>>>>>>>>>>>>>>>>>> conditions as inputs. >>>>>>>>>>>>>>>>>>>>> >> > > >>>>>>>>>>>>>>>>>>>>> >> > > I mean to say that generally in a given beam >>>>>>>>>>>>>>>>>>>>> bending problem, a diagram of a beam and distributed >>>>>>>>>>>>>>>>>>>>> loads are provided. So >>>>>>>>>>>>>>>>>>>>> it is not possible to get these data as an user input. >>>>>>>>>>>>>>>>>>>>> Rather we can expect >>>>>>>>>>>>>>>>>>>>> that the user would formulate the bending moment >>>>>>>>>>>>>>>>>>>>> function, in the form of >>>>>>>>>>>>>>>>>>>>> Singularity function, and then provide that function as >>>>>>>>>>>>>>>>>>>>> an input for >>>>>>>>>>>>>>>>>>>>> getting the elastic curve equation. >>>>>>>>>>>>>>>>>>>>> >> > > >>>>>>>>>>>>>>>>>>>>> >> > > Note:- Values of E , I , Boundary Conditions >>>>>>>>>>>>>>>>>>>>> are also expected as an input. >>>>>>>>>>>>>>>>>>>>> >> > > >>>>>>>>>>>>>>>>>>>>> >> > > I need your suggestions. >>>>>>>>>>>>>>>>>>>>> >> > > >>>>>>>>>>>>>>>>>>>>> >> > > >>>>>>>>>>>>>>>>>>>>> >> > > >>>>>>>>>>>>>>>>>>>>> >> > > ----------------- >>>>>>>>>>>>>>>>>>>>> >> > > Regards, >>>>>>>>>>>>>>>>>>>>> >> > > Sampad >>>>>>>>>>>>>>>>>>>>> >> > > >>>>>>>>>>>>>>>>>>>>> >> > > >>>>>>>>>>>>>>>>>>>>> >> > > >>>>>>>>>>>>>>>>>>>>> >> > > >>>>>>>>>>>>>>>>>>>>> >> > > >>>>>>>>>>>>>>>>>>>>> >> > > Regards >>>>>>>>>>>>>>>>>>>>> >> > > Sampad Kumar Saha >>>>>>>>>>>>>>>>>>>>> >> > > Mathematics and Computing >>>>>>>>>>>>>>>>>>>>> >> > > I.I.T. Kharagpur >>>>>>>>>>>>>>>>>>>>> >> > > >>>>>>>>>>>>>>>>>>>>> >> > > On Sat, Mar 12, 2016 at 11:50 AM, Aaron Meurer < >>>>>>>>>>>>>>>>>>>>> [email protected]> wrote: >>>>>>>>>>>>>>>>>>>>> >> > > It should give (-1)**n*f^(n)(0) (that is, >>>>>>>>>>>>>>>>>>>>> (-1)**n*diff(f(x), x, n).subs(x, 0)), if I remember the >>>>>>>>>>>>>>>>>>>>> formula correctly. >>>>>>>>>>>>>>>>>>>>> >> > > >>>>>>>>>>>>>>>>>>>>> >> > > Aaron Meurer >>>>>>>>>>>>>>>>>>>>> >> > > >>>>>>>>>>>>>>>>>>>>> >> > > On Fri, Mar 11, 2016 at 9:00 AM, SAMPAD SAHA < >>>>>>>>>>>>>>>>>>>>> [email protected]> wrote: >>>>>>>>>>>>>>>>>>>>> >> > > Hi Aaron, >>>>>>>>>>>>>>>>>>>>> >> > > >>>>>>>>>>>>>>>>>>>>> >> > > I have a doubt . >>>>>>>>>>>>>>>>>>>>> >> > > >>>>>>>>>>>>>>>>>>>>> >> > > Do we want: >>>>>>>>>>>>>>>>>>>>> >> > > >>>>>>>>>>>>>>>>>>>>> >> > > >>>>>>>>>>>>>>>>>>>>> >> > > integrate(f(x)*DiracDelta(x, n), (x, -oo, oo)) >>>>>>>>>>>>>>>>>>>>> would output as >>>>>>>>>>>>>>>>>>>>> >> > > >>>>>>>>>>>>>>>>>>>>> >> > > <image.png> >>>>>>>>>>>>>>>>>>>>> >> > > >>>>>>>>>>>>>>>>>>>>> >> > > >>>>>>>>>>>>>>>>>>>>> >> > > >>>>>>>>>>>>>>>>>>>>> >> > > >>>>>>>>>>>>>>>>>>>>> >> > > >>>>>>>>>>>>>>>>>>>>> >> > > Regards >>>>>>>>>>>>>>>>>>>>> >> > > Sampad Kumar Saha >>>>>>>>>>>>>>>>>>>>> >> > > Mathematics and Computing >>>>>>>>>>>>>>>>>>>>> >> > > I.I.T. Kharagpur >>>>>>>>>>>>>>>>>>>>> >> > > >>>>>>>>>>>>>>>>>>>>> >> > > On Wed, Mar 9, 2016 at 3:11 AM, Aaron Meurer < >>>>>>>>>>>>>>>>>>>>> [email protected]> wrote: >>>>>>>>>>>>>>>>>>>>> >> > > DiracDelta(x, k) gives the k-th derivative of >>>>>>>>>>>>>>>>>>>>> DiracDelta(x) (or you >>>>>>>>>>>>>>>>>>>>> >> > > can write DiracDelta(x).diff(x, k)). >>>>>>>>>>>>>>>>>>>>> >> > > >>>>>>>>>>>>>>>>>>>>> >> > > It does look like the delta integrate routines >>>>>>>>>>>>>>>>>>>>> could be improved here, though: >>>>>>>>>>>>>>>>>>>>> >> > > >>>>>>>>>>>>>>>>>>>>> >> > > In [2]: integrate(f(x)*DiracDelta(x), (x, -oo, >>>>>>>>>>>>>>>>>>>>> oo)) >>>>>>>>>>>>>>>>>>>>> >> > > Out[2]: f(0) >>>>>>>>>>>>>>>>>>>>> >> > > >>>>>>>>>>>>>>>>>>>>> >> > > In [3]: integrate(f(x)*DiracDelta(x, 1), (x, >>>>>>>>>>>>>>>>>>>>> -oo, oo)) >>>>>>>>>>>>>>>>>>>>> >> > > Out[3]: >>>>>>>>>>>>>>>>>>>>> >> > > ∞ >>>>>>>>>>>>>>>>>>>>> >> > > ⌠ >>>>>>>>>>>>>>>>>>>>> >> > > ⎮ f(x)⋅DiracDelta(x, 1) dx >>>>>>>>>>>>>>>>>>>>> >> > > ⌡ >>>>>>>>>>>>>>>>>>>>> >> > > -∞ >>>>>>>>>>>>>>>>>>>>> >> > > >>>>>>>>>>>>>>>>>>>>> >> > > Since the integration rules for derivatives of >>>>>>>>>>>>>>>>>>>>> delta functions are >>>>>>>>>>>>>>>>>>>>> >> > > simple extensions of the rules for the delta >>>>>>>>>>>>>>>>>>>>> function itself, this is >>>>>>>>>>>>>>>>>>>>> >> > > probably not difficult to fix. >>>>>>>>>>>>>>>>>>>>> >> > > >>>>>>>>>>>>>>>>>>>>> >> > > Aaron Meurer >>>>>>>>>>>>>>>>>>>>> >> > > >>>>>>>>>>>>>>>>>>>>> >> > > On Mon, Feb 29, 2016 at 3:39 AM, Tim Lahey < >>>>>>>>>>>>>>>>>>>>> [email protected]> wrote: >>>>>>>>>>>>>>>>>>>>> >> > > > Hi, >>>>>>>>>>>>>>>>>>>>> >> > > > >>>>>>>>>>>>>>>>>>>>> >> > > > Singularity functions are actually extremely >>>>>>>>>>>>>>>>>>>>> easy to implement given that we have a Dirac delta and >>>>>>>>>>>>>>>>>>>>> Heaviside functions. >>>>>>>>>>>>>>>>>>>>> Assuming that the Dirac delta and Heaviside functions >>>>>>>>>>>>>>>>>>>>> properly handle >>>>>>>>>>>>>>>>>>>>> calculus, it’s trivial to wrap them for use as >>>>>>>>>>>>>>>>>>>>> singularity functions. The >>>>>>>>>>>>>>>>>>>>> only thing that will need to be added is the derivative >>>>>>>>>>>>>>>>>>>>> of the Dirac delta >>>>>>>>>>>>>>>>>>>>> (assuming it’s not already there). I implemented >>>>>>>>>>>>>>>>>>>>> singularity functions in >>>>>>>>>>>>>>>>>>>>> Maple in less than an afternoon. >>>>>>>>>>>>>>>>>>>>> >> > > > >>>>>>>>>>>>>>>>>>>>> >> > > > I was a TA for a Mechanics of Deformable >>>>>>>>>>>>>>>>>>>>> Solids course about 11 or 12 times and wrote it to help >>>>>>>>>>>>>>>>>>>>> the students (as we >>>>>>>>>>>>>>>>>>>>> have a site license for Maple). I also wrote a set of >>>>>>>>>>>>>>>>>>>>> lecture notes on the >>>>>>>>>>>>>>>>>>>>> topic. >>>>>>>>>>>>>>>>>>>>> >> > > > >>>>>>>>>>>>>>>>>>>>> >> > > > Cheers, >>>>>>>>>>>>>>>>>>>>> >> > > > >>>>>>>>>>>>>>>>>>>>> >> > > > Tim. >>>>>>>>>>>>>>>>>>>>> >> > > > >>>>>>>>>>>>>>>>>>>>> >> > > >> On Feb 26, 2016, at 4:29 PM, SAMPAD SAHA < >>>>>>>>>>>>>>>>>>>>> [email protected]> wrote: >>>>>>>>>>>>>>>>>>>>> >> > > >> >>>>>>>>>>>>>>>>>>>>> >> > > >> Hi Jason, >>>>>>>>>>>>>>>>>>>>> >> > > >> >>>>>>>>>>>>>>>>>>>>> >> > > >> Thank you for the explanation. It really >>>>>>>>>>>>>>>>>>>>> helped me. >>>>>>>>>>>>>>>>>>>>> >> > > >> >>>>>>>>>>>>>>>>>>>>> >> > > >> So, basically we want to start it, firstly, >>>>>>>>>>>>>>>>>>>>> by creating a module which would deal with the >>>>>>>>>>>>>>>>>>>>> mathematical operations >>>>>>>>>>>>>>>>>>>>> performed on Singularity Functions. After this whole >>>>>>>>>>>>>>>>>>>>> module is prepared, we >>>>>>>>>>>>>>>>>>>>> would focus on how to use this module for solving beam >>>>>>>>>>>>>>>>>>>>> problems. Am I >>>>>>>>>>>>>>>>>>>>> correct? >>>>>>>>>>>>>>>>>>>>> >> > > >> >>>>>>>>>>>>>>>>>>>>> >> > > >> Can you please explain me in brief that what >>>>>>>>>>>>>>>>>>>>> are the mathematical operations we wanted to implement on >>>>>>>>>>>>>>>>>>>>> that module? >>>>>>>>>>>>>>>>>>>>> >> > > >> >>>>>>>>>>>>>>>>>>>>> >> > > >> >>>>>>>>>>>>>>>>>>>>> >> > > >> On Friday, February 26, 2016 at 4:54:59 PM >>>>>>>>>>>>>>>>>>>>> UTC+5:30, SAMPAD SAHA wrote: >>>>>>>>>>>>>>>>>>>>> >> > > >> >>>>>>>>>>>>>>>>>>>>> >> > > >> Hi, >>>>>>>>>>>>>>>>>>>>> >> > > >> >>>>>>>>>>>>>>>>>>>>> >> > > >> I am Sampad Kumar Saha , an Undergraduate >>>>>>>>>>>>>>>>>>>>> Mathematics and Computing Student at I.I.T. Kharagpur. >>>>>>>>>>>>>>>>>>>>> >> > > >> >>>>>>>>>>>>>>>>>>>>> >> > > >> I have gone through the idea page and I am >>>>>>>>>>>>>>>>>>>>> interested in working on the project named Singularity >>>>>>>>>>>>>>>>>>>>> Function. >>>>>>>>>>>>>>>>>>>>> >> > > >> >>>>>>>>>>>>>>>>>>>>> >> > > >> By going through the Idea, I understood that >>>>>>>>>>>>>>>>>>>>> we want to add a package to Sympy which can be used for >>>>>>>>>>>>>>>>>>>>> for solving beam >>>>>>>>>>>>>>>>>>>>> bending stress and deflection problems using singularity >>>>>>>>>>>>>>>>>>>>> function. Am I >>>>>>>>>>>>>>>>>>>>> correct? >>>>>>>>>>>>>>>>>>>>> >> > > >> >>>>>>>>>>>>>>>>>>>>> >> > > >> We can by this way:- >>>>>>>>>>>>>>>>>>>>> >> > > >> While solving we will be having the moment >>>>>>>>>>>>>>>>>>>>> function as an input which we can arrange in the form of >>>>>>>>>>>>>>>>>>>>> singularity >>>>>>>>>>>>>>>>>>>>> functions and then integrate it twice to get the >>>>>>>>>>>>>>>>>>>>> deflection curve and we >>>>>>>>>>>>>>>>>>>>> can give the plot or the equation obtained of deflection >>>>>>>>>>>>>>>>>>>>> curve as an output. >>>>>>>>>>>>>>>>>>>>> >> > > >> >>>>>>>>>>>>>>>>>>>>> >> > > >> I have gone through some documents available >>>>>>>>>>>>>>>>>>>>> on internet which have brief studies on solving beam >>>>>>>>>>>>>>>>>>>>> bending stress and >>>>>>>>>>>>>>>>>>>>> deflection problems using singularity functions. >>>>>>>>>>>>>>>>>>>>> >> > > >> >>>>>>>>>>>>>>>>>>>>> >> > > >> References:- >>>>>>>>>>>>>>>>>>>>> >> > > >> • Beam Deflection By Discontinuity >>>>>>>>>>>>>>>>>>>>> Functions. >>>>>>>>>>>>>>>>>>>>> >> > > >> • Beam Equation Using Singularity >>>>>>>>>>>>>>>>>>>>> Functions. >>>>>>>>>>>>>>>>>>>>> >> > > >> • Enhanced Student Learning in >>>>>>>>>>>>>>>>>>>>> Engineering Courses with CAS Technology. >>>>>>>>>>>>>>>>>>>>> >> > > >> Since there is just a brief idea given in >>>>>>>>>>>>>>>>>>>>> the idea page, I have a doubt that what are the things >>>>>>>>>>>>>>>>>>>>> other than solving >>>>>>>>>>>>>>>>>>>>> beam bending stress and deflection problems to be >>>>>>>>>>>>>>>>>>>>> implemented in the >>>>>>>>>>>>>>>>>>>>> project? >>>>>>>>>>>>>>>>>>>>> >> > > >> >>>>>>>>>>>>>>>>>>>>> >> > > >> Any type of suggestions are welcome. >>>>>>>>>>>>>>>>>>>>> >> > > >> >>>>>>>>>>>>>>>>>>>>> >> > > >> >>>>>>>>>>>>>>>>>>>>> ========================================================================================================================================== >>>>>>>>>>>>>>>>>>>>> >> > > >> Regards >>>>>>>>>>>>>>>>>>>>> >> > > >> Sampad Kumar Saha >>>>>>>>>>>>>>>>>>>>> >> > > >> Mathematics and Computing >>>>>>>>>>>>>>>>>>>>> >> > > >> I.I.T. Kharagpur >>>>>>>>>>>>>>>>>>>>> >> > > >> >>>>>>>>>>>>>>>>>>>>> >> > > >> -- >>>>>>>>>>>>>>>>>>>>> >> > > >> You received this message because you are >>>>>>>>>>>>>>>>>>>>> subscribed to the Google Groups "sympy" group. >>>>>>>>>>>>>>>>>>>>> >> > > >> To unsubscribe from this group and stop >>>>>>>>>>>>>>>>>>>>> receiving emails from it, send an email to >>>>>>>>>>>>>>>>>>>>> [email protected]. >>>>>>>>>>>>>>>>>>>>> >> > > >> To post to this group, send email to >>>>>>>>>>>>>>>>>>>>> [email protected]. >>>>>>>>>>>>>>>>>>>>> >> > > >> Visit this group at >>>>>>>>>>>>>>>>>>>>> https://groups.google.com/group/sympy. >>>>>>>>>>>>>>>>>>>>> >> > > >> To view this discussion on the web visit >>>>>>>>>>>>>>>>>>>>> https://groups.google.com/d/msgid/sympy/7cbe2101-fd59-484b-9e25-f563636d6366%40googlegroups.com >>>>>>>>>>>>>>>>>>>>> . >>>>>>>>>>>>>>>>>>>>> >> > > >> For more options, visit >>>>>>>>>>>>>>>>>>>>> https://groups.google.com/d/optout. >>>>>>>>>>>>>>>>>>>>> >> > > > 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>>>>>>>>>>>>>>>>>>>>> >> > To unsubscribe from this group and stop receiving >>>>>>>>>>>>>>>>>>>>> emails from it, send an email to >>>>>>>>>>>>>>>>>>>>> [email protected]. >>>>>>>>>>>>>>>>>>>>> >> > To post to this group, send email to >>>>>>>>>>>>>>>>>>>>> [email protected]. >>>>>>>>>>>>>>>>>>>>> >> > Visit this group at >>>>>>>>>>>>>>>>>>>>> https://groups.google.com/group/sympy. >>>>>>>>>>>>>>>>>>>>> >> > To view this discussion on the web visit >>>>>>>>>>>>>>>>>>>>> https://groups.google.com/d/msgid/sympy/B66DECFB-0205-41DC-A09D-342BBDF6FAC4%40gmail.com >>>>>>>>>>>>>>>>>>>>> . >>>>>>>>>>>>>>>>>>>>> >> > For more options, visit >>>>>>>>>>>>>>>>>>>>> https://groups.google.com/d/optout. >>>>>>>>>>>>>>>>>>>>> >> >>>>>>>>>>>>>>>>>>>>> >> >>>>>>>>>>>>>>>>>>>>> > >>>>>>>>>>>>>>>>>>>>> > >>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>> >>>>>>>>>>>>>> >>>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>> >>>>>>>>> >>>>>>>> >>>>>>> >>>>>> >>>>> >>>> >>> >> -- >> You received this message because you are subscribed to the Google Groups >> "sympy" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to [email protected]. >> To post to this group, send email to [email protected]. >> Visit this group at https://groups.google.com/group/sympy. >> To view this discussion on the web visit >> https://groups.google.com/d/msgid/sympy/CANzav4GGN1PyV%2B8ekiPKgEurqCHf15CU3HuoZYS3THoChL54PA%40mail.gmail.com >> <https://groups.google.com/d/msgid/sympy/CANzav4GGN1PyV%2B8ekiPKgEurqCHf15CU3HuoZYS3THoChL54PA%40mail.gmail.com?utm_medium=email&utm_source=footer> >> . >> >> For more options, visit https://groups.google.com/d/optout. >> > > > > -- > Regards > *Sartaj Singh* > > *Mathematics and Computing*, > Indian Institute of Technology, > Varanasi - 221 005 INDIA > > E-mail: [email protected], *[email protected] > <[email protected]>* > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at https://groups.google.com/group/sympy. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/CAC%2BH8-H43g%2BrjCZ5Oqv9oghKa9TVXT5goBX_HfaK4gb5L2twzA%40mail.gmail.com > <https://groups.google.com/d/msgid/sympy/CAC%2BH8-H43g%2BrjCZ5Oqv9oghKa9TVXT5goBX_HfaK4gb5L2twzA%40mail.gmail.com?utm_medium=email&utm_source=footer> > . > > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/sympy. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CANzav4EF_CkFHZ-furcZCmYkJk7ZH%3D5oZDqvZxUTTJHgogLQfQ%40mail.gmail.com. For more options, visit https://groups.google.com/d/optout.
